Concerted hydrogen-bond dynamics in the transport mechanism of the hydrated proton: a first-principles molecular dynamics study

Neural-network-based molecular dynamics simulations reveal that proton transport in water is doubly gated by sequential hydrogen-bond exchange

The transport of excess protons in water is central to acid-base chemistry, biochemistry and energy production. However, elucidating its mechanism has been challenging. Recent nonlinear vibrational spectroscopy experiments could not be explained by existing models. Here we use both vibrational spectroscopy calculations and neural-network-based molecular dynamics simulations that account for nuclear quantum effects for all atoms to determine the proton transport mechanism. Our simulations reveal an equilibrium between two stable proton-localized structures with distinct Eigen-like and Zundel-like hydrogen-bond motifs. Proton transport follows a three-step mechanism gated by two successive hydrogen-bond exchanges: the first reduces the proton-acceptor water coordination, leading to proton transfer, and the second, the rate-limiting step, prevents rapid back-transfer by increasing the proton-donor coordination. This sequential mechanism is consistent with experimental characterizations of proton diffusion, explaining the low activation energy and the prolonged intermediate lifetimes in vibrational spectroscopy. These results are crucial for understanding proton dynamics in biochemical and technological systems.

Reshaping the QM Region On-the-Fly: Adaptive-Shape QM/MM Dynamic Simulations of a Hydrated Proton in Bulk Water

Adaptive quantum mechanics/molecular mechanics (QM/MM) reclassifies on-the-fly a molecule or molecular fragment as QM or MM during dynamics simulations without abrupt changes in the energy or forces. Notably, the permuted adaptive-partitioning (PAP) algorithms have been applied to simulate a hydrated proton, with a mobile QM zone anchored at a pseudoatom called a proton indicator. The position of the proton indicator approximates the location of the delocalized excess proton, yielding a smooth trajectory of the proton diffusing via the Grotthuss mechanism in aqueous solutions. The mobile QM zone, which has been taken to be a sphere with a preset radius, follows the proton wherever it goes. Although the simulations are successful, the use of a spherical QM zone has one disadvantage: A large preset radius must be utilized to minimize the chance of missing water molecules that are important to proton translocation. A large radius leads to a large QM zone, which is computationally expensive. In this work, we report a new way to set up the QM zone, where one includes only the water molecules important to proton transfer. The importance of a given water molecule is quantified by its "weight" that depends on its relation to the reaction path of proton transfer. The weight varies smoothly, ensuring that a water molecule gradually appears in or disappears from the QM zone without abrupt changes, as required by the PAP method. Consequently, the shape of the QM zone evolves on-the-fly, keeping the QM zone as small as possible and as large as necessary. Test simulations demonstrate that the new algorithm significantly improves the computation efficiency while maintaining the proper descriptions of proton transfer in bulk water.

Superprotonic Conductivity in a Metalloporphyrin-Based SMOF (Supramolecular Metal-Organic Framework)

Metal-organic frameworks and supramolecular metal-organic frameworks (SMOFs) exhibit great potential for a broad range of applications taking advantage of the high surface area and pore sizes and tunable chemistry. In particular, metalloporphyrin-based MOFs and SMOFs are becoming of great importance in many fields due to the bioessential functions of these macrocycles that are being mimicked. On the other hand, during the last years, proton-conducting materials have aroused much interest, and those presenting high conductivity values are potential candidates to play a key role in some solid-state electrochemical devices such as batteries and fuel cells. In this way, using metalloporphyrins as building units we have obtained a new crystalline material with formula [H(bipy)]2[(MnTPPS)(H2O)2]·2bipy·14H2O, where bipy is 4,4'-bipyidine and TPPS4- is the meso-tetra(4-sulfonatephenyl) porphyrin. The crystal structure shows a zig-zag water chain along the [100] direction located between the sulfonate groups of the porphyrin. Taking into account those structural features, the compound was tested for proton conduction by complex electrochemical impedance spectroscopy (EIS). The as-obtained conductivity is 1 × 10-2 S·cm-1 at 40 °C and 98% relative humidity, which is a remarkably high value.

Investigating Intramolecular H Atom Transfer Dynamics in β-Diketones with Ultrafast Infrared Spectroscopies and Theoretical Modeling

The vibrational signatures and ultrafast dynamics of the intramolecular H-bond in a series of β-diketones are investigated with 2D IR spectroscopy and computational modeling. The chosen β-diketones exhibit a range of H atom donor-acceptor distances and asymmetry along the H atom transfer coordinate that tunes the intramolecular H-bond strength. The species with the strongest H-bonds are calculated to have very soft H atom potentials, resulting in highly red-shifted OH stretch fundamental frequencies and dislocation of the H atom upon vibrational excitation. These soft potentials lead to significant coupling to the other normal mode coordinates and give rise to the very broad vibrational signatures observed experimentally. The 2D IR spectra in both the OH and OD stretch regions of the light and deuterated isotopologues reveal broadened and long-lived ground-state bleach signatures of the vibrationally hot molecules. Polarization-sensitive transient absorption measurements in the OH and OD stretch regions reveal notable isotopic differences in orientational dynamics. Orientational relaxation was measured to occur on ∼600 fs and ∼2 ps time scales for the light and deuterated isotopologues, respectively. The orientational dynamics are interpreted in terms of activated H/D atom transfer events driven by collective intramolecular structural rearrangements.

Mechanistic Insights into Water Autoionization through Metadynamics Simulation Enhanced by Machine Learning

Characterizing the free energy landscape of water ionization has been a great challenge due to the limitations from expensive ab initio calculations and strong rare-event features. Lacking equilibrium sampling of the ionization pathway will cause ambiguities in the mechanistic study. Here, we obtain convergent free energy surfaces through nanosecond timescale metadynamics simulations with classical nuclei enhanced by atomic neural network potentials, which yields good reproduction of the equilibrium constant (pK_{w}=14.14) and ionization rate constant (1.369×10^{-3}  s^{-1}). The character of transition state unveils the triple-proton transfer occurs through a concerted but asynchronous mechanism. Conditional ensemble average analyses establish the dual-presolvation mechanism, where a pair of hypercoordinated and undercoordinated waters bridged by one H_{2}O cooperatively constitutes the initiation environment for autoionization, and contributes extremely to the local electric field fluctuation to promote water dissociation.

Comparison of classical and ab initio simulations of hydronium and aqueous proton transfer

Proton transport in aqueous systems occurs by making and breaking covalent bonds, a process that classical force fields cannot reproduce. Various attempts have been made to remedy this deficiency, by valence bond theory or instantaneous proton transfers, but the ability of such methods to provide a realistic picture of this fundamental process has not been fully evaluated. Here we compare an ab initio molecular dynamics (AIMD) simulation of an excess proton in water to a simulation of a classical H3O+ in TIP3P water. The energy gap upon instantaneous proton transfer from H3O+ to an acceptor water molecule is much higher in the classical simulation than in the AIMD configurations evaluated with the same classical potential. The origins of this discrepancy are identified by comparing the solvent structures around the excess proton in the two systems. One major structural difference is in the tilt angle of the water molecules that accept an hydrogen bond from H3O+. The lack of lone pairs in TIP3P produces a tilt angle that is too large and generates an unfavorable geometry after instantaneous proton transfer. This problem can be alleviated by the use of TIP5P, which gives a tilt angle much closer to the AIMD result. Another important factor that raises the energy gap is the different optimal distance in water-water vs H3O+-water H-bonds. In AIMD the acceptor is gradually polarized and takes a hydronium-like configuration even before proton transfer actually happens. Ways to remedy some of these problems in classical simulations are discussed.

Microscopic Mechanism of Proton Transfer in Pure Water under Ambient Conditions

Water molecules and the associated proton transfer (PT) are prevalent in chemical and biological systems and have been a hot research topic. Spectroscopic characterization and ab initio molecular dynamics (AIMD) simulations have previously revealed insights into acidic and basic liquids. Presumably, the situation in the acidic/basic solution is not necessarily the same as in pure water; in addition, the autoionization constant for water is only 10^-14 under ambient conditions, making the study of PT in pure water challenging. To overcome this issue, we modeled periodic water box systems containing 1000 molecules for tens of nanoseconds based on a neural network potential (NNP) with quantum mechanical accuracy. The NNP was generated by training a dataset containing the energies and atomic forces of 17 075 configurations of periodic water box systems, and these data points were calculated at the MP2 level that considers electron correlation effects. We found that the size of the system and the duration of the simulation have a significant impact on the convergence of the results. With these factors considered, our simulations showed that hydronium (H₃O⁺) and hydroxide (OH^-) ions in water have distinct hydration structures, thermodynamic and kinetic properties, e.g., the longer-lasting and more stable hydrated structure of OH^- ions than that of H₃O⁺, as well as a significantly higher free energy barrier for the OH^--associated PT than that of H₃O⁺, leading the two to exhibit completely different PT behaviors. Given these characteristics, we further found that PT via OH^- ions tends not to occur multiple times or between many molecules. In contrast, PT via H₃O⁺ can synergistically occur among multiple molecules and prefers to adopt a cyclic pattern among three water molecules, while it occurs mostly in a chain pattern when more water molecules are involved. Therefore, our studies provide a detailed and solid microscopic explanation for the PT process in pure water.

Search for a Grotthuss mechanism through the observation of proton transfer

The transport of protons is critical in a variety of bio- and electro-chemical processes and technologies. The Grotthuss mechanism is considered to be the most efficient proton transport mechanism, generally implying a transfer of protons between 'chains' of host molecules via elementary reactions within the hydrogen bonds. Although Grotthuss proposed this concept more than 200 years ago, only indirect experimental evidence of the mechanism has been observed. Here we report the first experimental observation of proton transfer between the molecules in pure and 85% aqueous phosphoric acid. Employing dielectric spectroscopy, quasielastic neutron, and light scattering, and ab initio molecular dynamic simulations we determined that protons move by surprisingly short jumps of only ~0.5-0.7 Å, much smaller than the typical ion jump length in ionic liquids. Our analysis confirms the existence of correlations in these proton jumps. However, these correlations actually reduce the conductivity, in contrast to a desirable enhancement, as is usually assumed by a Grotthuss mechanism. Furthermore, our analysis suggests that the expected Grotthuss-like enhancement of conductivity cannot be realized in bulk liquids where ionic correlations always decrease conductivity.

Mechanism of Cations Suppressing Proton Diffusion Kinetics for Electrocatalysis

Proton transfer is crucial for electrocatalysis. Accumulating cations at electrochemical interfaces can alter the proton transfer rate and then tune electrocatalytic performance. However, the mechanism for regulating proton transfer remains ambiguous. Here, we quantify the cation effect on proton diffusion in solution by hydrogen evolution on microelectrodes, revealing the rate can be suppressed by more than 10 times. Different from the prevalent opinions that proton transport is slowed down by modified electric field, we found water structure imposes a more evident effect on kinetics. FTIR test and path integral molecular dynamics simulation indicate that proton prefers to wander within the hydration shell of cations rather than to hop rapidly along water wires. Low connectivity of water networks disrupted by cations corrupts the fast-moving path in bulk water. This study highlights the promising way for regulating proton kinetics via a modified water structure.

Highly Altered State of Proton Transport in Acid Pools in Charged Reverse Micelles

Transport mechanisms of solvated protons of 1 M HCl acid pools, confined within reverse micelles (RMs) containing the negatively charged surfactant sodium bis(2-ethylhexyl) sulfosuccinate (NaAOT) or the positively charged cetyltrimethylammonium bromide (CTABr), are analyzed with reactive force field simulations to interpret dynamical signatures from TeraHertz absorption and dielectric relaxation spectroscopy. We find that the forward proton hopping events for NaAOT are further suppressed compared to a nonionic RM, while the Grotthuss mechanism ceases altogether for CTABr. We attribute the sluggish proton dynamics for both charged RMs as due to headgroup and counterion charges that expel hydronium and chloride ions from the interface and into the bulk interior, thereby increasing the pH of the acid pools relative to the nonionic RM. For charged NaAOT and CTABr RMs, the localization of hydronium near a counterion or conjugate base reduces the Eigen and Zundel configurations that enable forward hopping. Thus, localized oscillatory hopping dominates, an effect that is most extreme for CTABr in which the proton residence time increases dramatically such that even oscillatory hopping is slow.

Ab initio molecular dynamics study of proton transport in imidazolium-based ionic liquids with added imidazole

Development of efficient anhydrous proton-conducting materials would expand the operational temperature ranges of hydrogen fuels cells (HFCs) and eliminate their dependence on maintaining sufficient hydration levels to function efficiently. Protic ionic liquids (PILs), which have high ionic densities and low vapor pressures, have emerged as a potential material for proton conducting layers in HFCs. In this work, we investigate proton transport via the Grotthuss mechanism in 1-ethylimidazolium bis-(trifluoromethanesulfonyl)imide ([C₂HIm][TFSI]) protic ionic liquids with added imidazole (Im⁰) using ab initio molecular dynamics. In particular, we vary the composition of the systems studied from pure [C₂HIm][TFSI] to those where the mole fraction of Im⁰ is 0.67. Given the large difference in pK_a between C₂HIm⁺ and HTFSI, TFSI^- does not accept acidic protons from C₂HIm⁺; conversely, imidazolium (HIm⁺) and C₂HIm⁺ have very similar pK_a values, and thus Im⁰ can readily accept protons. We find that the unprotonated nitrogen on Im⁰ dominates solvation of the labile protons on C₂HIm⁺ and other Im⁰ species, resulting in formation of robust imidazole wires. Given the amphoteric nature of Im⁰, i.e. its ability to accept and donate protons, these wires provide conduits along which protons can rapidly traverse via the Grotthuss mechanism, thereby greatly increasing the proton coefficient of self-diffusion. We find that the average length of the wires increases with added Im⁰, and thus as the mole fraction of Im⁰ increases so too does the proton diffusion constant. Lastly, we analyze our trajectories to determine the energy and time scales associated with proton transfer.

Unraveling the Nature of Hydrogen Bonds of "Proton Sponges" Based on Car-Parrinello and Metadynamics Approaches

The nature of intra- and intermolecular non-covalent interactions was studied in four naphthalene derivatives commonly referred to as "proton sponges". Special attention was paid to an intramolecular hydrogen bond present in the protonated form of the compounds. The unsubstituted "proton sponge" served as a reference structure to study the substituent influence on the hydrogen bond (HB) properties. We selected three compounds substituted by methoxy, amino, and nitro groups. The presence of the substituents either retained the parent symmetry or rendered the compounds asymmetric. In order to reveal the non-covalent interaction properties, the Hirshfeld surface (HS) was computed for the crystal structures of the studied compounds. Next, quantum-chemical simulations were performed in vacuo and in the crystalline phase. Car-Parrinello molecular dynamics (CPMD), Path Integral Molecular Dynamics (PIMD), and metadynamics were employed to investigate the time-evolution changes of metric parameters and free energy profile in both phases. Additionally, for selected snapshots obtained from the CPMD trajectories, non-covalent interactions and electronic structure were studied. Quantum theory of atoms in molecules (QTAIM) and the Density Overlap Regions Indicator (DORI) were applied for this purpose. It was found based on Hirshfeld surfaces that, besides intramolecular hydrogen bonds, other non-covalent interactions are present and have a strong impact on the crystal structure organization. The CPMD results obtained in both phases showed frequent proton transfer phenomena. The proton was strongly delocalized in the applied time-scale and temperature, especially in the PIMD framework. The use of metadynamics allowed for tracing the free energy profiles and confirming that the hydrogen bonds present in "proton sponges" are Low-Barrier Hydrogen Bonds (LBHBs). The electronic and topological analysis quantitatively described the temperature dependence and time-evolution changes of the electronic structure. The covalency of the hydrogen bonds was estimated based on QTAIM analysis. It was found that strong hydrogen bonds show greater covalency, which is additionally determined by the proton position in the hydrogen bridge.

Tracking the Delocalized Proton in Concerted Proton Transfer in Bulk Water

A solvated proton in water is often characterized as a charge or structural defect, and it is important to track its evolution on-the-fly in certain dynamics simulations. Previously, we introduced the proton indicator, a pseudo-atom, whose position approximates the location of the excess proton modeled as a structural defect. The proton indicator generally yields a smooth trajectory of a hydrated proton diffusing in aqueous solutions, including in the events of stepwise proton transfer via the Grotthuss mechanism; however, the proton indicator did not perform well in the events of concerted proton transfer, for which it occasionally yielded large position displacements between two successive time steps. To overcome this hurdle, we develop a new algorithm of a proton indicator with greatly enhanced performance for concerted proton transfer in bulk water. A protocol is proposed to exhaustively explore the hydrogen-bonding network of the water wires over which the excess proton is delocalized and to properly account for the contributions of the water molecules in this network as the geometry evolves. The new proton indicator (called Indicator 2.0) is assessed in dynamics simulations of an excess proton in bulk water and in specially constructed model systems of more complex architectures. The results demonstrate that the new indicator yields a smooth trajectory in both stepwise and concerted proton transfers.

Modulation of Diffusion Mechanism and Its Correlation with Complexation in Aqueous Deep Eutectic Solvents

Aqueous mixtures of deep eutectic solvents (DESs) have gained traction recently as an effective template to tailor their physicochemical properties. But detailed microscopic insights into the effects of water on the molecular relaxation phenomenon in DESs are not entirely understood. DESs are strong network-forming liquids due to the extensive hydrogen bonding and complex formation between their species, and therefore, water can behave as a controlled disruptor altering the microscopic structure and dynamics in DESs. In this study, the role of water in the diffusion mechanism of acetamide in the aqueous mixtures of DESs synthesized using acetamide and lithium perchlorate is investigated using molecular dynamics (MD) simulation and quasielastic neutron scattering (QENS). The acetamide dynamics comprises localized diffusion within transient cages and a jump diffusion process across cages. The jump diffusion process is observed to be strongly enhanced by about a factor of 10 as the water content in the system is increased. Meanwhile, the geometry of the localized dynamics is unaltered by addition of water, but the localized diffusion becomes significantly faster and more heterogeneous with increasing water concentration. The accelerating effects of water on localized diffusion are also substantiated by QENS experiments. The water concentration in the DES is observed to control the solvation structure of lithium ions, with the ions becoming significantly hydrated at 20 wt % water. The formation of interwater and water-acetamide hydrogen bonds is observed. The increase in water concentration is found to increase the number of H-bonds; however, their lifetimes are found to decrease substantially. Similarly, the lifetimes of acetamide-lithium complexes are also found to be diminished by increasing water concentration. A power-law scaling relationship between lifetimes and diffusion constants is established, elucidating the extent of coupling between diffusive processes and hydrogen bonding and microscopic complexation. This study demonstrates the ability to use water as an agent to probe the role of structural relaxation and complex lifetimes of diffusive processes at different time and length scales.

Proton-transfer spectroscopy beyond the normal-mode scenario

A stochastic theory is developed to predict the spectral signature of proton-transfer processes and is applied to infrared spectra computed from ab initio molecular-dynamics simulations of a single [Formula: see text] cation. By constraining the oxygen atoms to a fixed distance, this system serves as a tunable model for general proton-transfer processes with variable barrier height. Three spectral contributions at distinct frequencies are identified and analytically predicted: the quasi-harmonic motion around the most probable configuration, amenable to normal-mode analysis, the contribution due to transfer paths when the proton moves over the barrier, and a shoulder for low frequencies stemming from the stochastic transfer-waiting-time distribution; the latter two contributions are not captured by normal-mode analysis but exclusively reported on the proton-transfer kinetics. In accordance with reaction rate theory, the transfer-waiting-contribution frequency depends inversely exponentially on the barrier height, whereas the transfer-path-contribution frequency is rather insensitive to the barrier height.

Spectral signatures of excess-proton waiting and transfer-path dynamics in aqueous hydrochloric acid solutions

The theoretical basis for linking spectral signatures of hydrated excess protons with microscopic proton-transfer mechanisms has so far relied on normal-mode analysis. We introduce trajectory-decomposition techniques to analyze the excess-proton dynamics in ab initio molecular-dynamics simulations of aqueous hydrochloric-acid solutions beyond the normal-mode scenario. We show that the actual proton transfer between two water molecules involves for relatively large water-water separations crossing of a free-energy barrier and thus is not a normal mode, rather it is characterized by two non-vibrational time scales: Firstly, the broadly distributed waiting time for transfer to occur with a mean value of 200-300 fs, which leads to a broad and weak shoulder in the absorption spectrum around 100 cm-1, consistent with our experimental THz spectra. Secondly, the mean duration of a transfer event of about 14 fs, which produces a rather well-defined spectral contribution around 1200 cm-1 and agrees in location and width with previous experimental mid-infrared spectra.

Structural and Dynamic Properties of Solvated Hydroxide and Hydronium Ions in Water from Ab Initio Modeling

Predicting the asymmetric structure and dynamics of solvated hydroxide and hydronium in water has been a challenging task from ab initio molecular dynamics (AIMD). The difficulty mainly comes from a lack of accurate and efficient exchange-correlation functional in elucidating the amphiphilic nature and the ubiquitous proton transfer behaviors of the two ions. By adopting the strongly-constrained and appropriately normed (SCAN) meta-GGA functional in AIMD simulations, we systematically examine the amphiphilic properties, the solvation structures, the electronic structures, and the dynamic properties of the two water ions. In particular, we compare these results to those predicted by the PBE0-TS functional, which is an accurate yet computationally more expensive exchange-correlation functional. We demonstrate that the general-purpose SCAN functional provides a reliable choice in describing the two water ions. Specifically, in the SCAN picture of water ions, the appearance of the fourth and fifth hydrogen bonds near hydroxide stabilizes the pot-like shape solvation structure and suppresses the structural diffusion, while the hydronium stably donates three hydrogen bonds to its neighbors. We apply a detailed analysis of the proton transfer mechanism of the two ions and find the two ions exhibit substantially different proton transfer patterns. Our AIMD simulations indicate hydroxide diffuses slower than hydronium in water, which is consistent with the experiments.

Revealing the Anticorrelation Behavior Mechanism between the Grotthuss and Vehicular Diffusions for Proton Transport in Concentrated Acid Solutions

In this study, we performed reactive molecular dynamics simulations to characterize proton solvation and transport in concentrated hydrochloric acid solutions. The correlation contribution to the total proton mean square displacement is found to be negative for all acid concentrations, indicating the anticorrelation between the Grotthuss and vehicular diffusions. For the vehicular diffusion, the hydronium ions tend to move freely toward the lone pair side independent of acid concentrations, whereas for the Grotthuss diffusion, the proton hopping direction is limited to one of the hydrogen-bonded water molecules on the opposite side of the lone pair region, which are specifically oriented with respect to the neighboring hydronium ion at higher acid concentrations. This result is justified by our findings of the higher fraction of proton rattling with the single hopping event and longer hydrogen bond lifetimes at higher acid concentrations. However, the angular distribution for both the vehicular and Grotthuss diffusions is found to be rather broad and comparable for all acid concentrations, and thus, the anticorrelation shows a minimal dependence on the acid concentration. Our results reveal that the anticorrelation behavior between the vehicle and Grotthuss diffusions is attributed to the amphiphilic nature of hydronium ions and thus is independent of the acid concentrations in solutions.

Bridging atomistic simulations and thermodynamic hydration models of aqueous electrolyte solutions

Chemical thermodynamic models of solvent and solute activities predict the equilibrium behavior of aqueous solutions. However, these models are semi-empirical. They represent micro-scale ion and solvent behaviors controlling the macroscopic properties using small numbers of parameters whose values are obtained by fitting to activities and other partial derivatives of the Gibbs energy measured for the bulk solutions. We have conducted atomistic simulations of aqueous electrolyte solutions (MgCl₂ and CaCl₂) to determine the parameters of thermodynamic hydration models. We have implemented a cooperative hydration model to categorize the water molecules in electrolyte solutions into different subpopulations. The value of the electrolyte-specific parameter, k, was determined from the ion-affected subpopulation with the lowest absolute value of the free energy of removing the water molecule. The other equilibrium constant parameter, K₁, associated with the first degree of hydration, was computed from the free energy of hydration of hydrated clusters. The hydration number, h, was determined from a reorientation dynamic analysis of the water subpopulations compared to bulk-like behavior. The reparameterized models [R. H. Stokes and R. H. Robinson, J. Solution Chem. 2, 173 (1973) and Balomenos et al., Fluid Phase Equilib. 243, 29 (2006)] using the computed values of the parameters lead to the osmotic coefficients of MgCl₂ solutions that are consistent with measurements. Such an approach removes the dependence on the availability of experimental data and could lead to aqueous thermodynamic models capable of estimating the values of solute and solvent activities as well as thermal and volumetric properties for a wide range of compositions and concentrations.

The Grotthuss mechanism for bifunctional proton transfer in poly(benzimidazole)

Poly(benzimidazole) (PBI) has received considerable attention as an effective high-temperature polymer electrolyte membrane for fuel cells. In this work, the Grotthuss mechanism for bifunctional proton transfer in PBI membranes was studied using density functional theory and transition state theory. This study focused on the reaction paths and kinetics for bifunctional proton transfer scenarios in neutral ([PBI]2), single (H+[PBI]2) and double-protonated (H2+[PBI]2) dimers. The theoretical results showed that the energy barriers and strength for H-bonds are sensitive to the local dielectric environment. For [PBI]2 with ε = 1, the uphill potential energy curve is attributed to extraordinarily strong ion-pair H-bonds in the transition structure, regarded as a 'dipolar energy trap'. For ε = 23, the ion-pair charges are partially neutralized, leading to a reduction in the electrostatic attraction in the transition structure. The dipolar energy trap appears to prohibit interconversion between the precursor, transition and proton-transferred structures, which rules out the possibility for [PBI]2 to be involved in the Grotthuss mechanism. For H+[PBI]2 and H2+[PBI]2 with ε = 1, the interconversion involves a low energy barrier, and the increase in the energy barrier for ε = 23 can be attributed to an increase in the strength of the protonated H-bonds in the transition structure: the local dielectric environment enhances the donor-acceptor interaction of the protonated H-bonds. Analysis of the rate constants confirmed that the quantum effect is not negligible for the N-H+ … N H-bond especially at low temperatures. Agreement between the theoretical and experimental data leads to the conclusion that the concerted bifunctional proton transfer in H2+[PBI]2 in a high local dielectric environment is 'the rate-determining scenario'. Therefore, a low local dielectric environment can be one of the required conditions for effective proton conduction in acid-doped PBI membranes. These theoretical results provide insights into the Grotthuss mechanism, which can be used as guidelines for understanding the fundamentals of proton transfers in other bifunctional H-bond systems.

Resolving the Structural Debate for the Hydrated Excess Proton in Water

It has long been proposed that the hydrated excess proton in water (aka the solvated "hydronium" cation) likely has two limiting forms, that of the Eigen cation (H₉O₄⁺) and that of the Zundel cation (H₅O₂⁺). There has been debate over which of these two is the more dominant species and/or whether intermediate (or "distorted") structures between these two limits are the more realistic representation. Spectroscopy experiments have recently provided further results regarding the excess proton. These experiments show that the hydrated proton has an anisotropy reorientation time scale on the order of 1-2 ps. This time scale has been suggested to possibly contradict the picture of the more rapid "special pair dance" phenomenon for the hydrated excess proton, which is a signature of a distorted Eigen cation. The special pair dance was predicted from prior computational studies in which the hydrated central core hydronium structure continually switches (O-H···O)* special pair hydrogen-bond partners with the closest three water molecules, yielding on average a distorted Eigen cation with three equivalent and dynamically exchanging distortions. Through state-of-art simulations it is shown here that anisotropy reorientation time scales of the same magnitude are obtained that also include structural reorientations associated with the special pair dance, leading to a reinterpretation of the experimental results. These results and additional analyses point to a distorted and dynamic Eigen cation as the most prevalent hydrated proton species in aqueous acid solutions of dilute to moderate concentration, as opposed to a stabilized or a distorted (but not "dancing") Zundel cation.

Dynamics and Surface Propensity of H+ and OH- within Rigid Interfacial Water: Implications for Electrocatalysis

Facile solvent reorganization promoting ion transfer across the solid-liquid interface is considered a prerequisite for efficient electrocatalysis. We provide first-principles insight into this notion by examining water self-ion dynamics at a highly rigid NaCl(100)-water interface. Through extensive density functional theory molecular dynamics simulations, we demonstrate for both acidic and alkaline solutions that Grotthuss dynamics is not impeded by a rigid water structure. Conversely, decreased proton transfer barriers and a striking propensity of H₃O⁺ and OH^- for stationary interfacial water are found. Differences in the ideal hydration structure of the ions, however, distinguish their behavior at the water contact layer. While hydronium can maintain its optimal solvation, the preferentially hypercoordinated hydroxide is repelled from the immediate vicinity of the surface due to interfacial coordination reduction. This has implications for alkaline hydrogen electrosorption in which the formation of undercoordinated OH^- at the surface is proposed to contribute to the observed sluggish kinetics.

Characterizing and Contrasting Structural Proton Transport Mechanisms in Azole Hydrogen Bond Networks Using Ab Initio Molecular Dynamics

Imidazole and 1,2,3-triazole are promising hydrogen-bonded heterocycles that conduct protons via a structural mechanism and whose derivatives are present in systems ranging from biological proton channels to proton exchange membrane fuel cells. Here, we leverage multiple time-stepping to perform ab initio molecular dynamics of imidazole and 1,2,3-triazole at the nanosecond time scale. We show that despite the close structural similarities of these compounds, their proton diffusion constants vary by over an order of magnitude. Our simulations reveal the reasons for these differences in diffusion constants, which range from the degree of hydrogen-bonded chain linearity to the effect of the central nitrogen atom in 1,2,3-triazole on proton transport. In particular, we uncover evidence of two "blocking" mechanisms in 1,2,3-triazole, where covalent and hydrogen bonds formed by the central nitrogen atom limit the mobility of protons. Our simulations thus provide insights into the origins of the experimentally observed 10-fold difference in proton conductivity.

Proton Traffic Jam: Effect of Nanoconfinement and Acid Concentration on Proton Hopping Mechanism

The properties of the water network in concentrated HCl acid pools in nanometer-sized reverse non-ionic micelles were probed with TeraHertz absorption, dielectric relaxation spectroscopy, and reactive force field simulations capable of describing proton hopping mechanisms. We identify that only at a critical micelle size of W0=9 do solvated proton complexes form in the water pool, accompanied by a change in mechanism from Grotthuss forward shuttling to one that favors local oscillatory hopping. This is due to a preference for H+ and Cl- ions to adsorb to the micelle interface, together with an acid concentration effect that causes a "traffic jam" in which the short-circuiting of the hydrogen-bonding motif of the hydronium ion decreases the forward hopping rate throughout the water interior even as the micelle size increases. These findings have implications for atmospheric chemistry, biochemical and biophysical environments, and energy materials, as transport of protons vital to these processes can be suppressed due to confinement, aggregation, and/or concentration.

The hopping mechanism of the hydrated excess proton and its contribution to proton diffusion in water

In this work, a series of analyses are performed on ab initio molecular dynamics simulations of a hydrated excess proton in water to quantify the relative occurrence of concerted hopping events and "rattling" events and thus to further elucidate the hopping mechanism of proton transport in water. Contrary to results reported in certain earlier papers, the new analysis finds that concerted hopping events do occur in all simulations but that the majority of events are the product of proton rattling, where the excess proton will rattle between two or more waters. The results are consistent with the proposed "special-pair dance" model of the hydrated excess proton wherein the acceptor water molecule for the proton transfer will quickly change (resonate between three equivalent special pairs) until a decisive proton hop occurs. To remove the misleading effect of simple rattling, a filter was applied to the trajectory such that hopping events that were followed by back hops to the original water are not counted. A steep reduction in the number of multiple hopping events is found when the filter is applied, suggesting that many multiple hopping events that occur in the unfiltered trajectory are largely the product of rattling, contrary to prior suggestions. Comparing the continuous correlation function of the filtered and unfiltered trajectories, we find agreement with experimental values for the proton hopping time and Eigen-Zundel interconversion time, respectively.

Binary structure and dynamics of the hydrogen bonds in the hydration shells of ions

Ion-specific effects of cations (Li+, Na+, K+, Mg2+, Ca2+) and anions (F-, Cl-) on the hydrogen bond structure and dynamics of the coordination waters in the hydration shells have been studied using molecular dynamics simulations. Our simulations indicate that the hydrogen bonds between the first and second hydration shell waters show binary structural and dynamic properties. The hydrogen bond with a first shell water as the donor (HD) is strengthened, while those with a first shell water as the acceptor (HA) are weakened. For a hydrated anion, this binary effect reverses, but is less significant. This ion-specific binary effect correlates with the size and the valence of the ion, and is more significant for the strong kosmotropic ions of high charge density.

OH- and H3O+ Diffusion in Model AEMs and PEMs at Low Hydration: Insights from Ab Initio Molecular Dynamics

Fuel cell-based anion-exchange membranes (AEMs) and proton exchange membranes (PEMs) are considered to have great potential as cost-effective, clean energy conversion devices. However, a fundamental atomistic understanding of the hydroxide and hydronium diffusion mechanisms in the AEM and PEM environment is an ongoing challenge. In this work, we aim to identify the fundamental atomistic steps governing hydroxide and hydronium transport phenomena. The motivation of this work lies in the fact that elucidating the key design differences between the hydroxide and hydronium diffusion mechanisms will play an important role in the discovery and determination of key design principles for the synthesis of new membrane materials with high ion conductivity for use in emerging fuel cell technologies. To this end, ab initio molecular dynamics simulations are presented to explore hydroxide and hydronium ion solvation complexes and diffusion mechanisms in the model AEM and PEM systems at low hydration in confined environments. We find that hydroxide diffusion in AEMs is mostly vehicular, while hydronium diffusion in model PEMs is structural. Furthermore, we find that the region between each pair of cations in AEMs creates a bottleneck for hydroxide diffusion, leading to a suppression of diffusivity, while the anions in PEMs become active participants in the hydronium diffusion, suggesting that the presence of the anions in model PEMs could potentially promote hydronium diffusion.

Water in biodegradable glucose–water–urea deep eutectic solvent: modifications of structure and dynamics in a crowded environment

Molecular dynamics simulations have been performed on a highly viscous (η ∼ 255 cP) naturally abundant deep eutectic solvent (NADES) composed of glucose, urea and water in a weight ratio of 6 : 4 : 1 at 328 K.

The "Hole" Story in Ionized Water from the Perspective of Ehrenfest Dynamics

The radiolysis of liquid water and the radiation-matter interactions that happen in aqueous environments are important to the fields of chemistry, materials, and environmental sciences, as well as the biological and physiological response to extreme conditions and medical treatments. The initial stage of radiolysis is the ultrafast response, or hole dynamics, that triggers chemical processes within complex energetic landscapes that may include reactivity. A fundamental understanding necessitates the use of theoretical methods that are capable of simulating both ultrafast coherence and non-adiabatic energy transfer pathways. In this work, we carry out an ab initio Ehrenfest dynamics study to provide a more complete description of the ultrafast dynamics and reactive events initiated by photoionization of water. After sudden ionization, a range of processes, including hole trapping and transfer, large OH oscillations, proton transfer and subsequent relay, formation of the metastable Zundel complex, and long-lived coherence, are identified and new insight into their driving forces is elucidated.

Decoding the 2D IR spectrum of the aqueous proton with high-level VSCF/VCI calculations

The aqueous proton is a common and long-studied species in chemistry, yet there is currently intense interest devoted to understanding its hydration structure and transport dynamics. Typically described in terms of two limiting structures observed in gas-phase clusters, the Zundel H₅O₂ ⁺ and Eigen H₉O₄ ⁺ ions, the aqueous structure is less clear due to the heterogeneity of hydrogen bonding environments and room-temperature structural fluctuations in water. The linear infrared (IR) spectrum, which reports on structural configurations, is challenging to interpret because it appears as a continuum of absorption, and the underlying vibrational modes are strongly anharmonically coupled to each other. Recent two-dimensional IR (2D IR) experiments presented strong evidence for asymmetric Zundel-like motifs in solution, but true structure-spectrum correlations are missing and complicated by the anharmonicity of the system. In this study, we employ high-level vibrational self-consistent field/virtual state configuration interaction calculations to demonstrate that the 2D IR spectrum reports on a broad distribution of geometric configurations of the aqueous proton. We find that the diagonal 2D IR spectrum around 1200 cm^-1 is dominated by the proton stretch vibrations of Zundel-like and intermediate geometries, broadened by the heterogeneity of aqueous configurations. There is a wide distribution of multidimensional potential shapes for the proton stretching vibration with varying degrees of potential asymmetry and confinement. Finally, we find specific cross peak patterns due to aqueous Zundel-like species. These studies provide clarity on highly debated spectral assignments and stringent spectroscopic benchmarks for future simulations.

Slowing Down of the Molecular Reorientation of Water in Concentrated Alkaline Solutions

It is generally accepted that the hydroxide ion (OH^-) is a strong hydrogen bond acceptor and that its anomalously high diffusion constant in water results from a Grotthuss-like structural diffusion mechanism. However, the spatial extent over which OH^- ions influence the dynamics of the hydrogen-bond network of water remained largely unclear. Here, we measure the ultrafast dynamics of OH groups of HDO molecules interacting with the deuterated hydroxide ion OD^-. For solutions with OD^- concentrations up to 4 M, we find that HDO molecules that are not directly interacting with the ions have a reorientation time constant of ∼2.7 ps, similar to that of pure liquid water. When the concentration of OD^- ions is increased, the reorientation time constant increases, indicating a strong slowing down of the structural dynamics of the solution.

How Can Protons Migrate in Extremely Compressed Liquid Water?

Compression of liquid water up to multi-kbar pressures is known to perturb dramatically its local structure required for charge defects to migrate as topological defects in the hydrogen-bonded network. Our ab initio simulations show that the migration of excess protons is not much affected at 10 kbar, whereas that of proton holes is significantly reduced. Non-Markovian analyses show that this is not due to modifying the free energy barriers of both charge transfer and migration. It is rather pressure-induced modifications of the population of activated states, depending on interstitial water, which rules charge migration at extreme compression.

Slow Proton Transfer in Nanoconfined Water

The transport of protons in nanoconfined environments, such as in nanochannels of biological or artificial proton conductive membranes, is essential to chemistry, biology, and nanotechnology. In water, proton diffusion occurs by hopping of protons between water molecules. This process involves the rearrangement of many hydrogen bonds and as such can be strongly affected by nanoconfinement. We study the vibrational and structural dynamics of hydrated protons in water nanodroplets stabilized by a cationic surfactant using polarization-resolved femtosecond infrared transient absorption spectroscopy. We determine the time scale of proton hopping in the center of the water nanodroplets from the dynamics of the anisotropy of the transient absorption signals. We find that in small nanodroplets with a diameter <4 nm, proton hopping is more than 10 times slower than in bulk water. Even in relatively large nanodroplets with a diameter of ∼7 nm, we find that the rate of proton hopping is slowed by ∼4 times compared with bulk water.

Understanding and Tracking the Excess Proton in Ab Initio Simulations; Insights from IR Spectra

Proton transport in aqueous media is ubiquitously important in chemical and biological processes. Although ab initio molecular dynamics (AIMD) simulations have made great progress in characterizing proton transport, there has been a long-standing challenge in defining and tracking the excess proton, or more properly, the center of excess charge (CEC) created when a hydrogen nucleus distorts the electron distributions of water molecules in a delocalized and highly dynamic nature. Yet, defining (and biasing) such a CEC is essential when combining AIMD with enhanced sampling methods to calculate the relevant macroscopic properties via free-energy landscapes, which is the standard practice for most processes of interest. Several CEC formulas have been proposed and used, but none have yet been systematically tested or rigorously derived. In this paper, we show that the CEC can be used as a computational tool to disentangle IR features of the solvated excess proton from its surrounding solvent, and in turn, how correlating the features in the excess charge spectrum with the behavior of CEC in simulations enables a systematic evaluation of various CEC definitions. We present a new definition of CEC and show how it overcomes the limitations of those currently available both from a spectroscopic point of view and from a practical perspective of performance in enhanced sampling simulations.

Interfacial solvation and slow transport of hydrated excess protons in non-ionic reverse micelles

This work employs molecular dynamics simulations to investigate the solvation and transport properties of hydrated excess protons (with a hydronium-like core structure) in non-ionic Igepal CO-520 reverse micelles of various sizes in a non-polar solvent. Multiscale Reactive Molecular Dynamics (MS-RMD) simulations were used to describe vehicular and hopping diffusion during the proton transport process. As detailed herein, an excess proton shows a marked tendency to localize in the interfacial region of micellar water pools. Slow proton transport was observed which becomes faster with increasing micellar size. Further analysis reveals that the slow diffusion of an excess proton is a combined result of slow water diffusion and the low proton hopping rate. This study also confirms that a low proton hopping rate in reverse micelles stems from the interfacial solvation of hydrated excess protons and the immobilization of interfacial water. The low water density in the interfacial region makes it difficult to form a complete hydrogen bond network near the hydrated excess proton, and therefore locks in the orientation of hydrated proton cations. The immobilization of the interfacial water also slows the relaxation of the overall hydrogen bond network.

Dynamical matrix propagator scheme for large-scale proton dynamics simulations

We derive a matrix formalism for the simulation of long range proton dynamics for extended systems and timescales. On the basis of an ab initio molecular dynamics simulation, we construct a Markov chain, which allows us to store the entire proton dynamics in an M × M transition matrix (where M is the number of oxygen atoms). In this article, we start from common topology features of the hydrogen bond network of good proton conductors and utilize them as constituent constraints of our dynamic model. We present a thorough mathematical derivation of our approach and verify its uniqueness and correct asymptotic behavior. We propagate the proton distribution by means of transition matrices, which contain kinetic data from both ultra-short (sub-ps) and intermediate (ps) timescales. This concept allows us to keep the most relevant features from the microscopic level while effectively reaching larger time and length scales. We demonstrate the applicability of the transition matrices for the description of proton conduction trends in proton exchange membrane materials.

Bulk-like and Interfacial Water Dynamics in Nafion Fuel Cell Membranes Investigated with Ultrafast Nonlinear IR Spectroscopy

The water confined in the hydrophilic domains of Nafion fuel cell membranes is central to its primary function of ion transport. Water dynamics are intimately linked to proton transfer and are sensitive to the structural features and length scales of confinement. Here, ultrafast polarization-selective pump-probe and two-dimensional infrared vibrational echo (2D IR) experiments were performed on fully hydrated Nafion membranes with sodium counterions to explicate the water dynamics. Like aerosol-OT reverse micelles (AOT RMs), the water dynamics in Nafion are attributed to bulk-like core water in the central region of the hydrophilic domains and much slower interfacial water. Population and orientational dynamics of water in Nafion are slowed by polymer confinement. Comparison of the observed dynamics to those of AOT RMs helps identify local interactions between water and sulfonate anions at the interface and among water molecules in the core. This comparison also demonstrates that the well-known spherical cluster morphology of Nafion is not appropriate. Spectral diffusion of the interfacial water, which arises from structural dynamics, was obtained from the 2D IR experiments taking the core water to have dynamics similar to bulk water. Like the orientational dynamics, spectral diffusion was found to be much slower at the interface compared to bulk water. Together, the dynamics indicate slow reorganization of weakly hydrogen-bonded water molecules at the interface of Nafion. These results provide insights into proton transport mechanisms in fuel cell membranes, and more generally, water dynamics near the interface of confining systems.

Hiding in the Crowd: Spectral Signatures of Overcoordinated Hydrogen-Bond Environments

Molecules with an excess number of hydrogen-bonding partners play a crucial role in fundamental chemical processes, ranging from anomalous diffusion in supercooled water to transport of aqueous proton defects and ordering of water around hydrophobic solutes. Here we show that overcoordinated hydrogen-bond environments can be identified in both the ambient and supercooled regimes of liquid water by combining experimental Raman multivariate curve resolution measurements and machine learning accelerated quantum simulations. In particular, we find that OH groups appearing in spectral regions usually associated with non-hydrogen-bonded species actually correspond to hydrogen bonds formed in overcoordinated environments. We further show that only these species exhibit a turnover in population as a function of temperature, which is robust and persists under both constant pressure and density conditions. This work thus provides a new tool to identify, interpret, and elucidate the spectral signatures of crowded hydrogen-bond networks.

The solvation effect on the rattling behaviour of the hydrated excess proton in water

The solvation effect on the kinetic rattling behaviour of the hydrated excess proton H⁺(aq) in water is theoretically modeled by using density functional theory (DFT) and the quantum chemical cluster model (CM). To test the solvation effects on the proton morphology and rattling kinetics, different solvation models for the proton are constructed based on the gas phase (GP) Zundel cation, which include the gas phase-polarizable continuum model (GP-PCM), the gas phase-supermolecule model (GP-SM), and the gas phase-supermolecule-polarizable continuum model (GP-SM-PCM). These solvation models consider either one or both of the short- and long-range solute-solvent interactions. Meanwhile, 1 to 6 explicit solvent water molecules (N_m' = 1-6) are added around the GP Zundel cation to test different explicit solvation environments. The calculation results show that the solvation environment has an important influence on the morphology and rattling kinetics of H⁺(aq). The proton rattling pathways are obtained only under the condition that both symmetrical explicit solvation environments and implicit bulk solvents are present. The zero-point contribution reduces the reaction energy barrier and enables the rattling to occur spontaneously at room temperature. The theoretical modeling results provide new insights into the microscopic kinetic behaviour of proton rattling in water at the molecular level, which are helpful in studying the proton transfer mechanism in aqueous systems.

Reduced rovibrational coupling Cartesian dynamics for semiclassical calculations: Application to the spectrum of the Zundel cation

We study the vibrational spectrum of the protonated water dimer, by means of a divide-and-conquer semiclassical initial value representation of the quantum propagator, as a first step in the study of larger protonated water clusters. We use the potential energy surface from the work of Huang et al. [J. Chem. Phys. 122, 044308 (2005)]. To tackle such an anharmonic and floppy molecule, we employ fully Cartesian dynamics and carefully reduce the coupling to global rotations in the definition of normal modes. We apply the time-averaging filter and obtain clean power spectra relative to suitable reference states that highlight the spectral peaks corresponding to the fundamental excitations of the system. Our trajectory-based approach allows for the physical interpretation of the very challenging proton transfer modes. We find that it is important, for such a floppy molecule, to selectively avoid initially exciting lower energy modes, in order to obtain cleaner spectra. The estimated vibrational energies display a mean absolute error (MAE) of ∼29 cm^-1 with respect to available multiconfiguration time-dependent Hartree calculations and MAE ∼ 14 cm^-1 when compared to the optically active experimental excitations of the Ne-tagged Zundel cation. The reasonable scaling in the number of trajectories for Monte Carlo convergence is promising for applications to higher dimensional protonated cluster systems.